Wednesday, June 25, 2008

Elearn Geometry Problem 130



See complete Problem 130
Triangle, Concurrent Cevians, Sum of Ratios. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

3 comments:

  1. can I know what is a cevian, please

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  2. A Cevian is any line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).

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  3. from an cevian theorem

    PD/AD + PE/BE + PF/FC = 1
    =>
    (AD - PA)/AD + (BE - PB)/BE + (FC - PC)/FC = 1

    AD/AD - PA/AD + BE/BE - PB/BE + FC/FC - PC/FC = 1

    1 - PA/AD + 1 - PB/BE + 1 - PC/FC = 1

    PA/AD + PB/BE + PC/FC = 2
    -------------------------------------------

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